Problem 28.

A car travels east at 89 km/h for 1 h. It then travels 26° east of north at 141 km/h for 1 h.

(a) What is the average speed for the trip?

(b) What is the average velocity for the trip?

Solution:

(a) The average speed is defined as the ratio of the total traveled distance and the traveled time. The total traveled distance is the sum of length AB (=89 km) and length BC (=141 km). The total traveled time is 2 hours. Then the average speed is

(b) The average velocity is defined as the ratio of the net displacement (the magnitude of the vector, connecting points A and C) and the traveled time (= 2 h)

We can find the length AC from the triangle ABC:

(cosine theorem).

Then the average velocity is